Electrolytes freezing point lowering

To calculate the freezing point lowering of an electrolyte in water, we use the general equation... 

Freezing point lowering (or other colligative properties) can be used to determine the extent of dissociation of a weak electrolyte in water. The procedure followed is illustrated in Example 10.11. 

Freezing point methods are often applied to the measurement of activities of electrolytes in dilute aqueous solution because the freezing point lowering, 6= T — T, can be determined with high accuracy, and the solute does not dissolve in the solid to any appreciable extent. Equations can be derivedgg relating a to 9 instead of T and T. The detailed expressions can be found in the literature.16... 

According to modem theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not indicate complete dissociation. For NaCl, the depression is not quite twice the amount calculated on the basis of the number of moles of NaCl added. In the solution, the ions attract one another to some extent therefore they do not behave as completely independent particles, as they would if they were nonelectrolytes. From the colligative properties, therefore, we can compute only the "apparent degree of dissociation" of a strong electrolyte in solution. 

The actual measurement of the freezing-point lowering caused by electrolytes has led us to choose the second postulate, that is, of the freedom of motion of the charged ions, as the nearer approximation to the true condition within the solution. 

The e> planation of the fact that a strong electrolyte such as potassium bromide produces a smaller freezing-point lowering than calculated for complete ionization is that there are strong electrical forces operating between the ions, which decrease their effectiveness, so that the properties of their solutions are different from those of ideal solutions, except at extreme dilution. The interionic attraction reduces the activity of the ions to a value less than their concentration. 

When electrolyte solutions are involved, however, the osmotic effects such as freezing point lowering, osmotic pressure increase, and rise in boiling point are much greater than corresponds to the total electrolyte concentration. Accordingly, van t Hoff introduced the irrationality factor i (van t Hoff factor) by which the particular osmotic effect could be divided to yield a number which satisfied the equation of state (i is always greater than 1). The van t Hoff factor is purely empirical and does not account for the anomalous behavior of strong electrolyte solutions. 

FREEZING POINT LOWERING BY ELECTROLYTES IN AQUEOUS SOLUTION... 

How many moles of each of the following strong electrolytes are needed to give the same freezing point lowering as... 

Freezing Point Lowering by Electrolytes in Aqueous Solution... 

The freezing points of electrolyte solutions, like their vapor pressures, are lower than those of nonelectrolytes at the same concentration. Sodium chloride and calcium chloride are used to lower the melting point of ice on highways their aqueous solutions can have freezing points as low as —21 and — 55°C, respectively. 

Freezing point The temperature at which the solid and liquid phases of a substance are at equilibrium, 269 electrolytes, 275 lowering, 277t... 

The presence of a solute lowers the freezing point of a solvent if the solute is nonvolatile, the boiling point is also raised. The freezing-point depression can be used to calculate the molar mass of the solute. If the solute is an electrolyte, the extent of its dissociation, protonation, or deprotonation must also be taken into account. 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

ATt is the number of degrees that the freezing point has been lowered (the difference in the freezing point of the pure solvent and the solution). Kt is the freezing-point depression constant (a constant of the individual solvent). The molality (m) is the molality of the solute, and i is the van t Hoff factor, which is the ratio of the number of moles of particles released into solution per mole of solute dissolved. For a nonelectrolyte such as sucrose, the van t Hoff factor would be 1. For an electrolyte such as sodium sulfate, you must take into consideration that if 1 mol of Na2S04 dissolves, 3 mol of particles would result (2 mol Na+, 1 mol SO) ). Therefore, the van t Hoff factor should be 3. However, because sometimes there is a pairing of ions in solution the observed van t Hoff factor is slightly less. The more dilute the solution, the closer the observed van t Hoff factor should be to the expected one. 

It can be observed that g is the ratio between the observed osmotic pressure and the osmotic pressure that would be observed for a completely dissociated electrolyte that follows Henry s law [see Equation (15.47)], hence the name, osmotic coefficient. A similar result can be obtained for the boiling point elevation, the freezing point depression, and the vapor pressure lowering. 

Binary electrolytes, such as KC1, although completely ionized, even in the solid state, lower the freezing point less than 2 x 1.86D, even when as dilute as I0-3M. This was at first attributed to incomplete ioni/aiion but is now explained by the long range of electrostatic forces. Note that Mg++ and SO4 are less independent than K+ and Cl- AgNOa, unlike KC1, etc., is a weak salt, and undissociated molecules increase rapidly with concentration. The ions nearer to an ion of one sign arc those of opposite sign, therefore electric conductivity is less than the sum of ionic conductivities extrapolated to zero concentration. 

The thermodynamic treatment of systems in which at least one component is an electrolyte needs special comment. Such systems present the first case where we must choose between treating the system in terms of components or in terms of species. No decision can be based on thermodynamics alone. If we choose to work in terms of components, any effect of the presence of new species that are different from the components, would appear in the excess chemical potentials. No error would be involved, and the thermodynamic properties of the system expressed in terms of the excess chemical potentials and based on the components would be valid. It is only when we wish to explain the observed behavior of a system, to treat the system on the basis of some theoretical concept or, possibly, to obtain additional information concerning the molecular properties of the system, that we turn to the concept of species. For example, we can study the equilibrium between a dilute aqueous solution of sodium chloride and ice in terms of the components water and sodium chloride. However, we know that the observed effect of the lowering of the freezing point of water is approximately twice that expected for a nondissociable solute. This effect is explained in terms of the ionization. In any given case the choice of the species is dictated largely by our knowledge of the system obtained outside of the field of thermodynamics and, indeed, may be quite arbitrary. 

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